Problem: Simplify the following expression: ${7(-6+9q)-(8q-7)}$
Explanation: Distribute the ${7}$ into the first set of parentheses: $ {7(}\gray{-6+9q}{)} - (8q-7) $ $ {-42+63q} - (8q-7) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ -42+63q {-1(}\gray{8q-7}{)} $ $ -42+63q {-8q+7} $ Rewrite the expression to group the ${q}$ terms and numeric terms: $ {63q - 8q} {-42 + 7}$ Combine the ${q}$ terms: $ {55q} {-42 + 7}$ Combine the numeric terms: $ {55q} {-35}$ The simplified expression is $55q-35$